Helmholtz charge layer

The potential between the Helmholtz double layer of a charged particle. Important for assessing the suitability of polyelectrolyte chemicals because it can be easily measured, unlike some other electrokinetic forces. 

Before constructing an electrode for microwave electrochemical studies, the question of microwave penetration in relation to the geometry of the sample has to be evaluated carefully. Typically only moderately doped semiconductors can be well investigated by microwave electrochemical techniques. On the other hand, if the microwaves are interacting with thin layers of materials or liquids also highly doped or even metallic films can be used, provided an appropriate geometry is selected to allow interaction of the microwaves with a thin oxide-, Helmholtz-, or space-charge layer of the materials. 

There are five possible physical phases in the current path in which the current conduction mechanisms are different as illustrated in Figure 19. They are substrate, space charge layer, Helmholtz layer, surface oxide film, and electrolyte. The overall change in the applied potential due to a change of current density in the current path is the sum of the potential drops in these phases ... 

Non-heavily doped p-Si Space charge layer Helmholtz layer space charge layer Oxide film... 

Because of the different potential distributions for different sets of conditions the apparent value of Tafel slope, about 60 mV, may have contributions from the various processes. The exact value may vary due to several factors which have different effects on the current-potential relationship 1) relative potential drops in the space charge layer and the Helmholtz layer 2) increase in surface area during the course of anodization due to formation of PS 3) change of the dissolution valence with potential 4) electron injection into the conduction band and 5) potential drops in the bulk semiconductor and electrolyte. 

The applied anodic potential may mostly or partially drop in the space charge layer or in the Helmholtz layer depending on doping type and concentration as well as on the potential range. 

For moderately doped substrates, when the surface is free of oxide the change of potential is mostly dropped in the space charge layer and in the Helmholtz double layer. The reactions are very sensitive to geometric factors. The reaction that is kinetically limited by the processes in the space charge layer is sensitive to radius of curvature, while that limited by the processes in the Helmholtz layer is sensitive to the orientation of the surface. Depending on the relative effect of each layer the curvature effect versus anisotropic effect can vary. 

The diffuse layer of excess electrons and holes in solids is called the space charge layer and the diffuse layer of excess hydrated ions in aqueous solution is simply called the diffuse layer and occasionally called the Gouy layer [Gouy, 1917]. The middle layer of adsorbed water moleciiles, between the diffuse layer on the aqueous solution side and the space charge layer on the soUd side, is called the compact or the inner layer. This compact or inner layer is also called the Helmholtz layer [Helmholtz, 1879] or the Stem layer [Stem, 1924] the plane of the closest approach of hydrated ions to the solid surface is called the outer Helmholtz plane (OHP) [Graham, 1947]. 

Fig. 5-8. Diffuse charge layer on the solution side of metal electrode M = electrode metal S = aqueous solution HL = compact layer (Helmholtz layer) DL = diffuse charge layer x distance from the outer Helmholtz plane (OHP).

The electron transfer reactions at the semiconductor/electrolyte interface occur either via the conduction band or the valence band. The total current is therefore given by the sum of four partial currents, denoted as represent electron transfer via the conduction anc valence bands, respectively, and the superscripts, a and c, indicate anodic anc cathodic processes, respectively. Let us assume nereafter that the electron transfer occurs only via the conduction band. In a simple case where the concentration of the electrolyte is sufficiently high and only the overvoltages at the Helmholtz layer (tjh) and in the space charge layer (rjsc) are important, the ica and cc can be given as follows4)... 

The unpinned band edges can move with applied potential, making the semiconductor electrode behave similar to a metal electrode in that changes in applied potential occur across the Helmholtz layer rather than across the semiconductor space charge layer. 

As seen in Figure 7, the effect of light on the system is to further increase the capacitance in the inversion layer. This, of course, enhances the unpinning effect as the capacitance of the space-charge-layer approaches or exceeds that of the Helmholtz 1ayer. 

It is possible to determine how surface states affect the distribution of potential in the interface if one assumes that the solution concerned is relatively concentrated so that the excess electric charge on the solution side of the interface is predominantly in the Helmholtz (H) layer. Then... 

Fig. 38. (a) Potential diagram (potential drop at the interfaces including the space charge layer Aipsc and Helmholtz layer Asemiconductor model of a metal with a n-type passive layer, with the band gap Eg, space charge layer dsc, conduction band CB, and valence band VB. 

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